March 30, 2021
Clinical trials are experiments. Correlation between treatment and health outcomes are causal (do not have confounding) assuming that…
TO THE BOARD
Does the efficacy of vaccines in clinical trials translate to real world use??
POLL
Might appear to be the only valid solution:
Experiments, under weak assumptions, let us find an unbiased causal relationship between X and Y
Internal Validity
A research design (choice of which cases to compare using correlation) has internal validity when the causal effect of X on Y it finds is not biased (systematically incorrect) / does not suffer from confounding.
What can we manipulate?
Who/what cases can we study?
External Validity
is the degree to which the causal relationship we find in a study captures/is relevant to the causal relationship in our causal question/claim
Study has external validity if the relationship found is true for the cases we are interested in
Study has external validity if the causal variable in the study maps onto the concept/definition of the cause in the causal claim.
More internal validity (unbiased calculation of causal effect) comes at the cost in external validity (relevance of study sample or cause to the theory)
Before we return to vaccination
You live in mid-19th century London.
What causes the spread of cholera?
Dominant view was that “miasmas” or bad air caused diseases like cholera
Snow mapped cholera deaths of 1854 outbreak in SoHo.
Critics pointed out:
Both might produce miasmas.
Snow’s solution to confounding: compare people “near pump” w/ different water sources
| Brewers | Broad St. Residents | |
|---|---|---|
| Water Source | Brewery Well/ Beer (Clean) |
Pump (Contam.) |
| Location | Near pump | Near pump |
| Timing | Aug. 1854 | Aug. 1854 |
| Miasmas? | Yes? | Yes? |
| Cholera | No | Yes |
Snow’s solution to confounding: compare people “far from pump” w/ different water sources
| Lady and Niece | Non-Soho Residents | |
|---|---|---|
| Water Source | Broad Street Pump (Contam.) |
Another Pump (Clean) |
| Location | Far from Broad St. | Far from Broad St. |
| Timing | Aug. 1854 | Aug. 1854 |
| Miasmas? | No | No |
| Cholera | Yes | No |
This solution to confounding is called…
when we observe \(X\) and \(Y\) for multiple cases, we examine the correlation of \(X\) and \(Y\) within groups of cases that are the same on confounding variables \(W, etc. \ldots\)
How does conditioning solve the problem?
Compare COVID infections between vaccinated and un-vaccinated, identical on…
Confounding: